"Dreams do come true-if you believe"

- Barno

ASSIGNMENT 05

MA260 Statistical Analysis I

NOTE: Show your work in the problems.

1. Compute the mean and variance of the following discrete probability distribution.

x P(x)

2 .50

8 .30

10 .20

2. The Computer Systems Department has eight faculty, six of whom are tenured. Dr. Vonder, the chair, wants to establish a committee of three department faculty members to review the curriculum. If she selects the committee at random:

a. What is the probability all members of the committee are tenured?

b. What is the probability that at least one member is not tenured? (Hint: For this question, use the complement rule.)

The probability that at least one is not tenured is the complement of the

probability that all three are tenured.

3. New Process, Inc., a large mail-order supplier of women’s fashions, advertises same-day service on every order. Recently, the movement of orders has not gone as planned, and there were a large number of complaints. Bud Owens, director of customer service, has completely redone the method of order handling. The goal is to have fewer than five unfilled orders on hand at the end of 95% of the working days. Frequent checks of the unfilled orders follow a Poisson distribution with a mean of two orders. Has New Process, Inc. lived up to its internal goal? Cite evidence.

The probability that the store has fewer than five unfilled orders is:

On average, the supplier can expect to have fewer than five unfilled orders on 94.73% of the working days. This is technically less than the 95% goal, but is extremely close. If the probability is rounded to the nearest whole percentage, then the supplier can expect to have fewer than five unfilled orders on 95% of the working days, thereby meeting their goal.

4. Recent information published by the U.S. Environmental Protection Agency indicates that Honda is the manufacturer of four of the top nine vehicles in terms of fuel economy.

a....

MA260 Statistical Analysis I

NOTE: Show your work in the problems.

1. Compute the mean and variance of the following discrete probability distribution.

x P(x)

2 .50

8 .30

10 .20

2. The Computer Systems Department has eight faculty, six of whom are tenured. Dr. Vonder, the chair, wants to establish a committee of three department faculty members to review the curriculum. If she selects the committee at random:

a. What is the probability all members of the committee are tenured?

b. What is the probability that at least one member is not tenured? (Hint: For this question, use the complement rule.)

The probability that at least one is not tenured is the complement of the

probability that all three are tenured.

3. New Process, Inc., a large mail-order supplier of women’s fashions, advertises same-day service on every order. Recently, the movement of orders has not gone as planned, and there were a large number of complaints. Bud Owens, director of customer service, has completely redone the method of order handling. The goal is to have fewer than five unfilled orders on hand at the end of 95% of the working days. Frequent checks of the unfilled orders follow a Poisson distribution with a mean of two orders. Has New Process, Inc. lived up to its internal goal? Cite evidence.

The probability that the store has fewer than five unfilled orders is:

On average, the supplier can expect to have fewer than five unfilled orders on 94.73% of the working days. This is technically less than the 95% goal, but is extremely close. If the probability is rounded to the nearest whole percentage, then the supplier can expect to have fewer than five unfilled orders on 95% of the working days, thereby meeting their goal.

4. Recent information published by the U.S. Environmental Protection Agency indicates that Honda is the manufacturer of four of the top nine vehicles in terms of fuel economy.

a....

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